Lots of techie stuff below. Dont feel obligated to read it. Or if you feel there is 'magic' involved and dont want to spoil anything....
Maybe freelook has some different engine settings, that would be unusual. Maybe its a bug in the engine that I never noticed. Would have to see it happen both in the mod and in a stock game also. To set it so a player is visible to some but not others requires deliberately hiding an entity entirely then looping through every player in the game and say 'show it me'.
Only a few things do this kind of thing. To get around asset limitations both modders and mappers will have multiple models in a single one. Both the Mig29 and F15 are in a single one for example each bound to a specific tag/joint. When launched the model is hidden to everybody in the game and the specific tag and its part is shown depending on which one of the two is needed. The UAV/CUAV does it also. The explosive decoy does it but twice since there are two crates. Each with a different part hidden. Friendlies see one (the trap) and enemies see the other (the decoy). MW2+ (or whichever has it) uses the two-crate method also. Change teams and it is all updated.
For the RC, since cod4 isnt meant to handle vehicles in MP it requires a work around where there are two entities. The player/owner and a separate car model. The player model itself is changed to the car and the player hidden to everybody. However there is an engine thing. Players always see themselves in third person even if hidden. The other entity, the 2nd car model, is shown to everyone in the game 'except' the owner. He only sees himself. Enemies are shooting and damaging the 2nd car not the player since he is fully hidden. If you look very closely at a fast moving car you can see it 'jitter' a little. Unfortunately that is engine related and cannot be fixed.
For those that remember, this was also the way to remove the problem of enemies shooting a car that has an invisible player above it. You couldnt damage the car because the invisible player model (torso, legs) hitbox was in the way. The convenient thing to do would have been to change the hitbox model. But because of hackers fucking it up for everybody the ability to do that was removed from MP entirely in one of the patches. But hiding a player globally also hides the hitbox. Which allows for the 2nd car to be shot. Because this is an obvious workaround when the RC/Predator/AC130/GBU24 ends the player is restored in several places with multiple-redundancy to make absolutely sure it is done correctly.